%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SYO462^3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:50:09 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 178 ( 47 unt; 0 typ; 8 def)
% Number of atoms : 1365 ( 238 equ; 0 cnn)
% Maximal formula atoms : 11 ( 7 avg)
% Number of connectives : 1685 ( 343 ~; 370 |; 0 &; 899 @)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% Number of symbols : 66 ( 62 usr; 15 con; 0-4 aty)
% ( 65 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 304 ( 0 sgn 56 !; 0 ?; 304 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mu: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
meq_ind: mu > mu > $i > $o ).
thf(func_def_1,type,
meq_prop: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_3,type,
mnot: ( $i > $o ) > $i > $o ).
thf(func_def_4,type,
mor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_5,type,
mand: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_6,type,
mimplies: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_7,type,
mimplied: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_8,type,
mequiv: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_9,type,
mxor: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_10,type,
mforall_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_11,type,
mforall_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_12,type,
mexists_ind: ( mu > $i > $o ) > $i > $o ).
thf(func_def_13,type,
mexists_prop: ( ( $i > $o ) > $i > $o ) > $i > $o ).
thf(func_def_14,type,
mtrue: $i > $o ).
thf(func_def_15,type,
mfalse: $i > $o ).
thf(func_def_16,type,
mbox: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_17,type,
mdia: ( $i > $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_18,type,
mreflexive: ( $i > $i > $o ) > $o ).
thf(func_def_19,type,
msymmetric: ( $i > $i > $o ) > $o ).
thf(func_def_20,type,
mserial: ( $i > $i > $o ) > $o ).
thf(func_def_21,type,
mtransitive: ( $i > $i > $o ) > $o ).
thf(func_def_22,type,
meuclidean: ( $i > $i > $o ) > $o ).
thf(func_def_23,type,
mpartially_functional: ( $i > $i > $o ) > $o ).
thf(func_def_24,type,
mfunctional: ( $i > $i > $o ) > $o ).
thf(func_def_25,type,
mweakly_dense: ( $i > $i > $o ) > $o ).
thf(func_def_26,type,
mweakly_connected: ( $i > $i > $o ) > $o ).
thf(func_def_27,type,
mweakly_directed: ( $i > $i > $o ) > $o ).
thf(func_def_28,type,
mvalid: ( $i > $o ) > $o ).
thf(func_def_29,type,
minvalid: ( $i > $o ) > $o ).
thf(func_def_30,type,
msatisfiable: ( $i > $o ) > $o ).
thf(func_def_31,type,
mcountersatisfiable: ( $i > $o ) > $o ).
thf(func_def_32,type,
rel_m: $i > $i > $o ).
thf(func_def_33,type,
mbox_m: ( $i > $o ) > $i > $o ).
thf(func_def_34,type,
mdia_m: ( $i > $o ) > $i > $o ).
thf(func_def_35,type,
p: $i > $o ).
thf(func_def_36,type,
q: $i > $o ).
thf(func_def_37,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_38,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_39,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_40,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_41,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_42,type,
vNOT: $o > $o ).
thf(func_def_43,type,
vOR: $o > $o > $o ).
thf(func_def_44,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_48,type,
vIMP: $o > $o > $o ).
thf(func_def_49,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
vAND: $o > $o > $o ).
thf(func_def_51,type,
db4:
!>[X0: $tType] : X0 ).
thf(f3,axiom,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mnot) ).
thf(f4,axiom,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mor) ).
thf(f5,axiom,
( mand
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mnot @ ( mor @ ( mnot @ X0 ) @ ( mnot @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mand) ).
thf(f6,axiom,
( mimplies
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mor @ ( mnot @ X0 ) @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mimplies) ).
thf(f8,axiom,
( mequiv
= ( ^ [X0: $i > $o,X1: $i > $o] : ( mand @ ( mimplies @ X0 @ X1 ) @ ( mimplies @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mequiv) ).
thf(f28,axiom,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^0.ax',mvalid) ).
thf(f32,axiom,
( mbox_m
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_m @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL013^3.ax',mbox_m) ).
thf(f35,conjecture,
mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove) ).
thf(f36,negated_conjecture,
~ ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) ),
inference(negated_conjecture,[status(cth)],[f35]) ).
thf(f39,plain,
( mnot
= ( ^ [X0: $i > $o,X1: $i] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f40,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[],[f39]) ).
thf(f41,plain,
( mor
= ( ^ [X0: $i > $o,X1: $i > $o,X2: $i] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f42,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[],[f41]) ).
thf(f43,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f5]) ).
thf(f44,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f46,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f8]) ).
thf(f80,plain,
( mvalid
= ( ^ [X0: $i > $o] :
! [X1: $i] : ( X0 @ X1 ) ) ),
inference(rectify,[],[f28]) ).
thf(f81,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f80]) ).
thf(f88,plain,
( mbox_m
= ( ^ [X0: $i > $o,X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
| ~ ( rel_m @ X1 @ X2 ) ) ) ),
inference(rectify,[],[f32]) ).
thf(f89,plain,
( mbox_m
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[],[f88]) ).
thf(f93,plain,
~ ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f94,plain,
( ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) )
!= $true ),
inference(fool_elimination,[],[f93]) ).
thf(f95,plain,
( ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) )
!= $true ),
inference(flattening,[],[f94]) ).
thf(f98,plain,
( mnot
= ( ^ [Y0: $i > $o,Y1: $i] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[],[f40]) ).
thf(f99,plain,
( mor
= ( ^ [Y0: $i > $o,Y1: $i > $o,Y2: $i] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[],[f42]) ).
thf(f100,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mnot @ ( mor @ ( mnot @ Y0 ) @ ( mnot @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f43]) ).
thf(f101,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mor @ ( mnot @ Y0 ) @ Y1 ) ) ),
inference(cnf_transformation,[],[f44]) ).
thf(f103,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] : ( mand @ ( mimplies @ Y0 @ Y1 ) @ ( mimplies @ Y1 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f46]) ).
thf(f123,plain,
( mvalid
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f81]) ).
thf(f127,plain,
( mbox_m
= ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[],[f89]) ).
thf(f130,plain,
( ( mvalid @ ( mimplies @ ( mbox_m @ ( mequiv @ p @ q ) ) @ ( mequiv @ ( mbox_m @ p ) @ ( mbox_m @ q ) ) ) )
!= $true ),
inference(cnf_transformation,[],[f95]) ).
thf(f133,plain,
( mand
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y1 ) ) ) ) ),
inference(definition_unfolding,[],[f100,f98,f99,f98,f98]) ).
thf(f134,plain,
( mimplies
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 ) ) ),
inference(definition_unfolding,[],[f101,f99,f98]) ).
thf(f136,plain,
( mequiv
= ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) ) ) ),
inference(definition_unfolding,[],[f103,f133,f134,f134]) ).
thf(f144,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o,Y4: $i] :
( ( Y2 @ Y4 )
| ( Y3 @ Y4 ) )
@ ( ^ [Y2: $i > $o,Y3: $i] :
~ ( Y2 @ Y3 )
@ Y0 )
@ Y1 )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ p
@ q ) )
@ ( ^ [Y0: $i > $o,Y1: $i > $o] :
( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ ( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y3 ) ) )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y0
@ Y1 )
@ ( ^ [Y2: $i > $o,Y3: $i > $o] :
( ^ [Y4: $i > $o,Y5: $i > $o,Y6: $i] :
( ( Y4 @ Y6 )
| ( Y5 @ Y6 ) )
@ ( ^ [Y4: $i > $o,Y5: $i] :
~ ( Y4 @ Y5 )
@ Y2 )
@ Y3 )
@ Y1
@ Y0 ) )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ p )
@ ( ^ [Y0: $i > $o,Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ~ ( rel_m @ Y1 @ Y2 )
| ( Y0 @ Y2 ) ) )
@ q ) ) ) ) ),
inference(definition_unfolding,[],[f130,f123,f134,f127,f136,f136,f127,f127]) ).
thf(f145,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f144]) ).
thf(f146,plain,
( $false
= ( ^ [Y0: $i] :
( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ~ ( ~ ( ~ ( p @ Y1 )
| ( q @ Y1 ) )
| ~ ( ~ ( q @ Y1 )
| ( p @ Y1 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( q @ Y1 ) ) )
| ( !! @ $i
@ ^ [Y1: $i] :
( ~ ( rel_m @ Y0 @ Y1 )
| ( p @ Y1 ) ) ) ) ) )
@ sK0 ) ),
inference(sigma_proxy_clausification,[],[f145]) ).
thf(f147,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f146]) ).
thf(f148,plain,
( $false
= ( ~ ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f149,plain,
( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f147]) ).
thf(f150,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f149]) ).
thf(f151,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ~ ( ~ ( ~ ( p @ Y0 )
| ( q @ Y0 ) )
| ~ ( ~ ( q @ Y0 )
| ( p @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f150]) ).
thf(f152,plain,
! [X1: $i] :
( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f151]) ).
thf(f153,plain,
! [X1: $i] :
( ( $true
= ( ~ ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f152]) ).
thf(f154,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) )
| ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f153]) ).
thf(f155,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( q @ X1 )
| ( p @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f156,plain,
! [X1: $i] :
( ( $false
= ( ~ ( ~ ( p @ X1 )
| ( q @ X1 ) ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f154]) ).
thf(f157,plain,
! [X1: $i] :
( ( $true
= ( ~ ( p @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f156]) ).
thf(f158,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f157]) ).
thf(f159,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) )
| ( $true
= ( ~ ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f158]) ).
thf(f160,plain,
! [X1: $i] :
( ( $false
= ( rel_m @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) )
| ( $false
= ( p @ X1 ) ) ),
inference(not_proxy_clausification,[],[f159]) ).
thf(f161,plain,
! [X1: $i] :
( ( $true
= ( ~ ( q @ X1 )
| ( p @ X1 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f155]) ).
thf(f162,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f161]) ).
thf(f163,plain,
! [X1: $i] :
( ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) )
| ( $true
= ( ~ ( q @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f162]) ).
thf(f164,plain,
! [X1: $i] :
( ( $false
= ( rel_m @ sK0 @ X1 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( q @ X1 ) ) ),
inference(not_proxy_clausification,[],[f163]) ).
thf(f165,plain,
( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f148]) ).
thf(f166,plain,
( ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f165]) ).
thf(f167,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f166]) ).
thf(f168,plain,
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f169,plain,
( ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f167]) ).
thf(f170,plain,
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f169]) ).
thf(f171,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(pi_proxy_clausification,[],[f170]) ).
thf(f172,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f171]) ).
thf(f173,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f174,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f172]) ).
thf(f175,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f174]) ).
thf(f176,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X2 ) ) ),
inference(pi_proxy_clausification,[],[f175]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X2 )
| ( p @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f176]) ).
thf(f178,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X2 )
| ( p @ X2 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f177]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X2 ) ) ) ),
inference(or_proxy_clausification,[],[f178]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f179]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) )
| ( $false
= ( rel_m @ sK0 @ X2 ) ) ),
inference(not_proxy_clausification,[],[f180]) ).
thf(f182,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK1 ) ) ),
inference(sigma_proxy_clausification,[],[f173]) ).
thf(f183,plain,
! [X1: $i] :
( ( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ( q @ X1 ) ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK1 )
| ( q @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f182]) ).
thf(f184,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK1 )
| ( q @ sK1 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f183]) ).
thf(f185,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f186,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK1 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f184]) ).
thf(f187,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_m @ sK0 @ sK1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f186]) ).
thf(f188,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $true
= ( rel_m @ sK0 @ sK1 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f187]) ).
thf(f189,plain,
! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( q @ sK1 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f185]) ).
thf(f190,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ~ ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ) ),
inference(sigma_proxy_clausification,[],[f168]) ).
thf(f191,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) )
| ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f190]) ).
thf(f192,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f193,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ) ),
inference(or_proxy_clausification,[],[f191]) ).
thf(f194,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) ) ) ) ),
inference(not_proxy_clausification,[],[f193]) ).
thf(f195,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $true
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ X1 ) ) ),
inference(pi_proxy_clausification,[],[f194]) ).
thf(f196,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_m @ sK0 @ sK2 )
| ( p @ sK2 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f195]) ).
thf(f197,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f198,plain,
! [X1: $i] :
( ( $false
= ( ~ ( rel_m @ sK0 @ sK2 ) ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f196]) ).
thf(f199,plain,
! [X1: $i] :
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 )
| ( p @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f198]) ).
thf(f200,plain,
! [X1: $i] :
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f199]) ).
thf(f201,plain,
! [X1: $i] :
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f200]) ).
thf(f202,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $true
= ( ~ ( rel_m @ sK0 @ X1 ) ) ) ),
inference(or_proxy_clausification,[],[f197]) ).
thf(f203,plain,
! [X1: $i] :
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( p @ X1 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) ) ),
inference(not_proxy_clausification,[],[f202]) ).
thf(f204,plain,
( ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( p @ Y0 ) )
@ sK2 ) )
| ( $false
= ( ^ [Y0: $i] :
( ~ ( rel_m @ sK0 @ Y0 )
| ( q @ Y0 ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f192]) ).
thf(f205,plain,
( ( $false
= ( ~ ( rel_m @ sK0 @ sK2 )
| ( p @ sK2 ) ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(beta-eta_normalization,[],[f204]) ).
thf(f206,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f207,plain,
( ( $false
= ( ~ ( rel_m @ sK0 @ sK2 ) ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f205]) ).
thf(f208,plain,
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK3 )
| ( q @ sK3 ) ) ) ),
inference(not_proxy_clausification,[],[f207]) ).
thf(f209,plain,
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( $false
= ( q @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f210,plain,
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f208]) ).
thf(f211,plain,
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ( $true
= ( rel_m @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f210]) ).
thf(f212,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( q @ sK3 ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f213,plain,
( ( $false
= ( p @ sK2 ) )
| ( $false
= ( ~ ( rel_m @ sK0 @ sK3 ) ) ) ),
inference(or_proxy_clausification,[],[f206]) ).
thf(f214,plain,
( ( $false
= ( p @ sK2 ) )
| ( $true
= ( rel_m @ sK0 @ sK3 ) ) ),
inference(not_proxy_clausification,[],[f213]) ).
thf(f219,definition,
( spl4_1
<=> ! [X2: $i] :
( ( $true
= ( p @ X2 ) )
| ( $false
= ( rel_m @ sK0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
thf(f220,plain,
( ! [X2: $i] :
( ( $false
= ( rel_m @ sK0 @ X2 ) )
| ( $true
= ( p @ X2 ) ) )
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f219]) ).
thf(f222,definition,
( spl4_2
<=> ! [X1: $i] :
( ( $true
= ( q @ X1 ) )
| ( $false
= ( rel_m @ sK0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
thf(f223,plain,
( ! [X1: $i] :
( ( $false
= ( rel_m @ sK0 @ X1 ) )
| ( $true
= ( q @ X1 ) ) )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f224,plain,
( spl4_1
| spl4_2 ),
inference(avatar_split_clause,[],[f181,f222,f219]) ).
thf(f226,definition,
( spl4_3
<=> ( $true
= ( rel_m @ sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
thf(f228,plain,
( ( $true
= ( rel_m @ sK0 @ sK1 ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f226]) ).
thf(f229,plain,
( spl4_3
| spl4_2 ),
inference(avatar_split_clause,[],[f188,f222,f226]) ).
thf(f231,definition,
( spl4_4
<=> ( $false
= ( q @ sK1 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
thf(f233,plain,
( ( $false
= ( q @ sK1 ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[],[f231]) ).
thf(f234,plain,
( spl4_4
| spl4_2 ),
inference(avatar_split_clause,[],[f189,f222,f231]) ).
thf(f236,definition,
( spl4_5
<=> ( $true
= ( rel_m @ sK0 @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
thf(f238,plain,
( ( $true
= ( rel_m @ sK0 @ sK2 ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f236]) ).
thf(f239,plain,
( spl4_1
| spl4_5 ),
inference(avatar_split_clause,[],[f201,f236,f219]) ).
thf(f241,definition,
( spl4_6
<=> ( $false
= ( p @ sK2 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
thf(f243,plain,
( ( $false
= ( p @ sK2 ) )
| ~ spl4_6 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f244,plain,
( spl4_1
| spl4_6 ),
inference(avatar_split_clause,[],[f203,f241,f219]) ).
thf(f246,definition,
( spl4_7
<=> ( $true
= ( rel_m @ sK0 @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_7])],[avatar_definition]) ).
thf(f248,plain,
( ( $true
= ( rel_m @ sK0 @ sK3 ) )
| ~ spl4_7 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f249,plain,
( spl4_7
| spl4_5 ),
inference(avatar_split_clause,[],[f211,f236,f246]) ).
thf(f251,definition,
( spl4_8
<=> ( $false
= ( q @ sK3 ) ) ),
introduced(definition,[new_symbols(definition,[spl4_8])],[avatar_definition]) ).
thf(f253,plain,
( ( $false
= ( q @ sK3 ) )
| ~ spl4_8 ),
inference(avatar_component_clause,[],[f251]) ).
thf(f254,plain,
( spl4_8
| spl4_5 ),
inference(avatar_split_clause,[],[f209,f236,f251]) ).
thf(f255,plain,
( spl4_7
| spl4_6 ),
inference(avatar_split_clause,[],[f214,f241,f246]) ).
thf(f256,plain,
( spl4_8
| spl4_6 ),
inference(avatar_split_clause,[],[f212,f241,f251]) ).
thf(f269,plain,
( ( $true = $false )
| ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(constrained_superposition,[],[f238,f223]) ).
thf(f272,plain,
( ( $true
= ( q @ sK2 ) )
| ~ spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f279,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5 ),
inference(constrained_superposition,[],[f238,f164]) ).
thf(f282,plain,
( ( $true
= ( p @ sK2 ) )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f295,plain,
( ( $true = $false )
| ( $false
= ( q @ sK2 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f282,f243]) ).
thf(f296,plain,
( ( $false
= ( q @ sK2 ) )
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f295]) ).
thf(f307,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(constrained_superposition,[],[f296,f272]) ).
thf(f313,plain,
( $false
| ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f307]) ).
thf(f314,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f313]) ).
thf(f330,plain,
( ( $true = $false )
| ( $true
= ( p @ sK2 ) )
| ~ spl4_1
| ~ spl4_5 ),
inference(constrained_superposition,[],[f220,f238]) ).
thf(f339,plain,
( ( $true
= ( p @ sK2 ) )
| ~ spl4_1
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f343,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(forward_demodulation,[],[f339,f243]) ).
thf(f344,plain,
( $false
| ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(trivial_inequality_removal,[],[f343]) ).
thf(f345,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(avatar_contradiction_clause,[],[f344]) ).
thf(f369,plain,
( ( $true = $false )
| ( $true
= ( p @ sK1 ) )
| ~ spl4_1
| ~ spl4_3 ),
inference(constrained_superposition,[],[f220,f228]) ).
thf(f370,plain,
( ( $true = $false )
| ( $true
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3 ),
inference(constrained_superposition,[],[f160,f228]) ).
thf(f373,plain,
( ( $true
= ( q @ sK1 ) )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f374,plain,
( ( $true
= ( p @ sK1 ) )
| ~ spl4_1
| ~ spl4_3 ),
inference(trivial_inequality_removal,[],[f369]) ).
thf(f378,plain,
( ( $true = $false )
| ( $false
= ( p @ sK1 ) )
| ~ spl4_3
| ~ spl4_4 ),
inference(forward_demodulation,[],[f373,f233]) ).
thf(f379,plain,
( ( $false
= ( p @ sK1 ) )
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f378]) ).
thf(f385,plain,
( ( $true = $false )
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(constrained_superposition,[],[f379,f374]) ).
thf(f391,plain,
( $false
| ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(trivial_inequality_removal,[],[f385]) ).
thf(f392,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(avatar_contradiction_clause,[],[f391]) ).
thf(f418,plain,
( ( $true = $false )
| ( $true
= ( q @ sK3 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(constrained_superposition,[],[f248,f223]) ).
thf(f433,plain,
( ( $true
= ( q @ sK3 ) )
| ~ spl4_2
| ~ spl4_7 ),
inference(trivial_inequality_removal,[],[f418]) ).
thf(f441,plain,
( ( $true = $false )
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(forward_demodulation,[],[f433,f253]) ).
thf(f442,plain,
( $false
| ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(trivial_inequality_removal,[],[f441]) ).
thf(f443,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(avatar_contradiction_clause,[],[f442]) ).
cnf(s1,plain,
( spl4_1
| spl4_2 ),
inference(sat_conversion,[],[f224]) ).
cnf(s2,plain,
( spl4_2
| spl4_3 ),
inference(sat_conversion,[],[f229]) ).
cnf(s3,plain,
( spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f234]) ).
cnf(s4,plain,
( spl4_1
| spl4_5 ),
inference(sat_conversion,[],[f239]) ).
cnf(s5,plain,
( spl4_1
| spl4_6 ),
inference(sat_conversion,[],[f244]) ).
cnf(s6,plain,
( spl4_5
| spl4_7 ),
inference(sat_conversion,[],[f249]) ).
cnf(s7,plain,
( spl4_5
| spl4_8 ),
inference(sat_conversion,[],[f254]) ).
cnf(s8,plain,
( spl4_6
| spl4_7 ),
inference(sat_conversion,[],[f255]) ).
cnf(s9,plain,
( spl4_6
| spl4_8 ),
inference(sat_conversion,[],[f256]) ).
cnf(s14,plain,
( ~ spl4_2
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f314]) ).
cnf(s16,plain,
( ~ spl4_1
| ~ spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f345]) ).
cnf(s24,plain,
( ~ spl4_1
| ~ spl4_3
| ~ spl4_4 ),
inference(sat_conversion,[],[f392]) ).
cnf(s26,plain,
( ~ spl4_2
| ~ spl4_7
| ~ spl4_8 ),
inference(sat_conversion,[],[f443]) ).
cnf(s27,plain,
spl4_1,
inference(rat,[],[s14,s1,s4,s5]) ).
cnf(s28,plain,
( spl4_6
| ~ spl4_2 ),
inference(rat,[],[s26,s8,s9]) ).
cnf(s29,plain,
~ spl4_2,
inference(rat,[],[s26,s6,s7,s16,s28,s27]) ).
cnf(s30,plain,
spl4_4,
inference(rat,[],[s3,s29]) ).
cnf(s31,plain,
spl4_3,
inference(rat,[],[s2,s29]) ).
cnf(s32,plain,
$false,
inference(rat,[],[s24,s27,s30,s31]) ).
thf(f444,plain,
$false,
inference(avatar_sat_refutation,[],[s32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO462^3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n011.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 16:59:01 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.28 Running first-order model finding
% 0.09/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.24/0.33 % (356278)Will run a generic schedule for satisfiability detection.
% 0.24/0.33 % (356284)% WARNING: option uhcvi not known.
% 0.24/0.33 % (356284)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2540100354:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.24/0.33 % (356283)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1197799969_2999 on theBenchmark for (2999ds/0Mi)
% 0.24/0.33 % (356284)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.33 % (356284)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.24/0.33 % Exception at run slice level
% 0.24/0.33 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.24/0.33 % (356284) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-356278-356284"...
% 0.24/0.33 % (356286)dis+10_1_sil=32000:sp=arity:random_seed=1607848014:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.24/0.33 % (356285)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=96701053:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.24/0.33 % (356287)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2820673946:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.24/0.33 % (356288)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4213696220:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.24/0.33 % (356289)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2377018124:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.24/0.33 % (356284)...printing done.
% 0.24/0.33 % (356287)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.24/0.33 % (356284)Refutation found. Thanks to Tanya!
% 0.24/0.33 % SZS status Theorem for theBenchmark
% 0.24/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.33 % (356284)------------------------------
% 0.24/0.33 % (356284)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (356284)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (356284)CaDiCaL version: 2.1.3
% 0.24/0.33 % (356284)Termination reason: Refutation
% 0.24/0.33 % (356284)Time elapsed: 0.015 s
% 0.24/0.33 % (356284)Peak memory usage: 13 MB
% 0.24/0.33 % (356284)Instructions burned: 30 (million)
% 0.24/0.33 % (356278)Success in time 0.039 s
% 0.24/0.33 % Vampire exiting
%------------------------------------------------------------------------------